compiler/stdc/math/ld80/e_coshl.c

   1 /* @(#)e_cosh.c 5.1 93/09/24 */
   2 /*
   3  * ====================================================
   4  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   5  *
   6  * Developed at SunPro, a Sun Microsystems, Inc. business.
   7  * Permission to use, copy, modify, and distribute this
   8  * software is freely granted, provided that this notice
   9  * is preserved.
  10  * ====================================================
  11  */
  12
  13 /* coshl(x)
  14  * Method :
  15  * mathematically coshl(x) if defined to be (exp(x)+exp(-x))/2
  16  *      1. Replace x by |x| (coshl(x) = coshl(-x)).
  17  *      2.
  18  *                                                      [ exp(x) - 1 ]^2
  19  *          0        <= x <= ln2/2  :  coshl(x) := 1 + -------------------
  20  *                                                         2*exp(x)
  21  *
  22  *                                                 exp(x) +  1/exp(x)
  23  *          ln2/2    <= x <= 22     :  coshl(x) := -------------------
  24  *                                                         2
  25  *          22       <= x <= lnovft :  coshl(x) := expl(x)/2
  26  *          lnovft   <= x <= ln2ovft:  coshl(x) := expl(x/2)/2 * expl(x/2)
  27  *          ln2ovft  <  x           :  coshl(x) := huge*huge (overflow)
  28  *
  29  * Special cases:
  30  *      coshl(x) is |x| if x is +INF, -INF, or NaN.
  31  *      only coshl(0)=1 is exact for finite x.
  32  */
  33
  34 #include "math.h"
  35
  36 #include "math_private.h"
  37
  38 static const long double one = 1.0, half=0.5, huge = 1.0e4900L;
  39
  40 long double
  41 coshl(long double x)
  42 {
  43         long double t,w;
  44         int32_t ex;
  45         uint32_t mx,lx;
  46
  47     /* High word of |x|. */
  48         GET_LDOUBLE_WORDS(ex,mx,lx,x);
  49         ex &= 0x7fff;
  50
  51     /* x is INF or NaN */
  52         if(ex==0x7fff) return x*x;
  53
  54     /* |x| in [0,0.5*ln2], return 1+expm1l(|x|)^2/(2*expl(|x|)) */
  55         if(ex < 0x3ffd || (ex == 0x3ffd && mx < 0xb17217f7u)) {
  56             t = expm1l(fabsl(x));
  57             w = one+t;
  58             if (ex<0x3fbc) return w;    /* cosh(tiny) = 1 */
  59             return one+(t*t)/(w+w);
  60         }
  61
  62     /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
  63         if (ex < 0x4003 || (ex == 0x4003 && mx < 0xb0000000u)) {
  64                 t = expl(fabsl(x));
  65                 return half*t+half/t;
  66         }
  67
  68     /* |x| in [22, ln(maxdouble)] return half*exp(|x|) */
  69         if (ex < 0x400c || (ex == 0x400c && mx < 0xb1700000u))
  70                 return half*expl(fabsl(x));
  71
  72     /* |x| in [log(maxdouble), log(2*maxdouble)) */
  73         if (ex == 0x400c && (mx < 0xb174ddc0u
  74                              || (mx == 0xb174ddc0u && lx < 0x31aec0ebu)))
  75         {
  76             w = expl(half*fabsl(x));
  77             t = half*w;
  78             return t*w;
  79         }
  80
  81     /* |x| >= log(2*maxdouble), cosh(x) overflow */
  82         return huge*huge;
  83 }